1.) Добро пожаловать в «Вася Пупкин и Ко». Наша телефонная горячая линия не работает во время праздников. Наш график работы можно найти на нашем сайте www.joendoe.de – Благодарим вас за оказанное доверие. Желаем вам и вашим близким приятных праздников и счастливого Нового года.
I thought it was funny but could never get away with using something like that at my org. I loved the “competent people who work for me” part – I make this joke all the time. We have some people who feel that they should have a manager personally attend to them and, at least in my case, my highly competent team is in the weeds of that work a lot more and are not rusty (like I am).

This makes a lot of sense to me, since surely in the 3-4 months people tend take as leave in the US, your issue would have been resolved. Also for parental leave, most people delegate ongoing projects to some specific person, so anything that’s still going to be going on months from now when you return is getting handled by someone else.
As with all winter breaks, but especially in a longer break, division and department leaders are responsible for ensuring that external contacts are aware of the closures and as appropriate salaried staff are performing services as necessary to meet the needs of the community during the closure, including checking email/voicemail and responding to time-sensitive matters.